If 6th, 12th and 18th terms of a GP are P, Q and R respectively, then prove that P, Q and R are in G.P.

2 answers

Let's say a,b then
GM=
ab

=24 or ab=576
a=
b
576



HM=
a+b
2ab

=
5
72



a+b
2×576

=
5
72



We get
a+b=80

On substituting the value of a,
b
576

+b−80=0

b
2
−80b+576=0
b=
2×1
+80±
80
2
−4×1×576





b=40±32
b=8, 72
a=72,8
If the common ratio of the GR is r, then
Q/P = r^6
R/Q = r^6
since there is a common ratio (R/Q = Q/P), P,Q,R form a GP